The Premier League club had said earlier in the day that the Argentina striker had handed them written notice of his desire to leave but that it had been turned down with Tevez later releasing a statement saying the situation was regrettable.
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"It is something I have felt for some time and have spent many hours thinking this through," the 26-year-old forward said in a statement reported by local media.
"Now I need to clear my head and think because this is an important part of my career. My feelings have not changed and it is regrettable that we have reached this situation.
"My relationship with certain executives and individuals at the club has broken down and is now beyond repair. I do not wish to expand on this at this stage. They know, because I have told them."
Newspaper reports had suggested a rift with manager Roberto Mancini but Tevez denied this was the case.
"I wish to clarify that I have no personal issue with the manager Roberto Mancini," said Tevez, who also thanked the club's owner Sheikh Mansour for his understanding and support.
City, who went joint top of the league on Saturday, said they were disappointed by Tevez's request, particularly as they had been so accommodating of his personal circumstances of his family living in South America.
"This is both an unfortunate and unwelcome distraction and the club will remain focused on the games ahead in what is turning out to be a very promising season," the club said in a statement on its website.
"The door remains open for Carlos to be selected to play."
Tevez, who joined City in 2009 after a spell at Manchester United and is the club's highest-paid player, missed Saturday's 3-1 victory at former club West Ham United through suspension.
FEELING HOMESICK
He has been enjoying some of the best form of his career at City, scoring 33 goals in 50 league appearances, and his desire to leave comes as more of a disappointment than a shock to fans given reports he is feeling homesick.
He has often spoken of his desire to return to South America and in August he hinted that he could even consider retiring from the game, such was his dismay at Argentina's defeat by Germany in the World Cup quarter-finals.
"I wanted to leave in the summer, but was convinced to return to the club. Sadly, my feelings have not changed," he said.
City singled out his representative, Kia Joorabchian, for criticism, saying they were disappointed "particularly with the actions of Carlos' representative" - a move that angered Tevez.
"I hugely resent the management's suggestions that I have been unduly influenced
